Trigonometry Examples

{log}_{2} (x) = y

$\log_{2} (x) = y$

Step 1

Find the asymptotes.

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Step 1.1

Switch sides.

y = {log}_{2} (x)

$y = \log_{2} (x)$

Step 1.2

Set the argument of the logarithm equal to zero.

x = 0

$x = 0$

Step 1.3

The vertical asymptote occurs at

x = 0

$x = 0$ .

Vertical Asymptote:

x = 0

$x = 0$

Vertical Asymptote:

x = 0

$x = 0$

Step 2

Find the point at

x = 1

$x = 1$ .

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Step 2.1

Replace the variable

x

$x$ with

1

$1$ in the expression.

f (1) = y

$f (1) = y$

Step 2.2

The final answer is

y

$y$ .

y

$y$

Step 2.3

Convert

y

$y$ to decimal.

y = y

$y = y$

y = y

$y = y$

Step 3

The log function can be graphed using the vertical asymptote at

x = 0

$x = 0$ and the points

(1, y), (2, y), (3, y)

$(1, y), (2, y), (3, y)$ .

Vertical Asymptote:

x = 0

$x = 0$

\begin{matrix} x & y 1 & y 2 & y 3 & y \end{matrix}

$\begin{array}{c} x & y \\ 1 & y \\ 2 & y \\ 3 & y \end{array}$

Step 4